# std::exp, std::expf, std::expl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float exp ( float num ); double exp ( double num ); long double exp ( long double num ); |  | (until C++23)
/*floating-point-type*/ exp ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float expf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double expl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> exp ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double exp ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes e (Euler's number, 2.7182818...) raised to the given power num. The library provides overloads of `std::exp` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::exp` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the base-e exponential of num (enum
) is returned.

If a range error occurs due to overflow, +HUGE_VAL, `+HUGE_VALF`, or `+HUGE_VALL` is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is ±0, 1 is returned.
- If the argument is -∞, +0 is returned.
- If the argument is +∞, +∞ is returned.
- If the argument is NaN, NaN is returned.

### Notes

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num, and underflow is guaranteed if num < -708.4.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::exp(num) has the same effect as std::exp(static_cast<double>(num)).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cmath>
    #include <cstring>
    #include <iomanip>
    #include <iostream>
    #include <numbers>

    // #pragma STDC FENV_ACCESS ON

    consteval double approx_e()
    {
        long double e{1.0};
        for (auto fac{1ull}, n{1llu}; n != 18; ++n, fac *= n)
            e += 1.0 / fac;
        return e;
    }

    int main()
    {
        std::cout << std::setprecision(16)
                  << "exp(1) = e¹ = " << std::exp(1) << '\n'
                  << "numbers::e  = " << std::numbers::e << '\n'
                  << "approx_e    = " << approx_e() << '\n'
                  << "FV of $100, continuously compounded at 3% for 1 year = "
                  << std::setprecision(6) << 100 * std::exp(0.03) << '\n';

        // special values
        std::cout << "exp(-0) = " << std::exp(-0.0) << '\n'
                  << "exp(-Inf) = " << std::exp(-INFINITY) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "exp(710) = " << std::exp(710) << '\n';

        if (errno == ERANGE)
            std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_OVERFLOW))
            std::cout << "    FE_OVERFLOW raised\n";
    }

Possible output:

    exp(1) = e¹ = 2.718281828459045
    numbers::e  = 2.718281828459045
    approx_e    = 2.718281828459045
    FV of $100, continuously compounded at 3% for 1 year = 103.045
    exp(-0) = 1
    exp(-Inf) = 0
    exp(710) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### See also

exp2exp2fexp2l (C++11)(C++11)(C++11) | returns 2 raised to the given power (\({\small 2^x}\)2x) (function)
expm1expm1fexpm1l (C++11)(C++11)(C++11) | returns e raised to the given power, minus 1 (\({\small e^x-1}\)ex-1) (function)
loglogflogl (C++11)(C++11) | computes natural (base e) logarithm (\({\small\ln{x}}\)ln(x)) (function)
exp(std::complex) | complex base e exponential (function template)
exp(std::valarray) | applies the function std::exp to each element of valarray (function template)
C documentation for exp

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